Recently, in connection with the progress toward higher integration in semiconductor devices, higher precision in aspherical lenses, etc., there is a growing need for manufacturing machines and measuring machines for the semiconductor devices and aspherical lens molds to ensure high shape (dimensional) accuracy and high long-term stability of shape accuracy.
The above ultra-precision machines require a precision mirror as a mirror for positioning or a reference mirror for reflection of laser or extreme ultraviolet rays. Therefore, such a mirror is being increasingly required to have both ultrahigh precision level, and dimensional long-term stability.
Zero-expansion glass is known as a conventional material for the mirror. The zero-expansion glass can be polish-finished to have a significantly smooth surface having an average surface roughness (Ra) of 1 nm or less. However, the zero-expansion glass has a low elastic modulus (Young's modulus) of 50 to 90 GPa, which leads to a problem of dead-weight deformation or deformation resulting from acceleration. Moreover, it is known that a zero-expansion glass material exhibits a significantly large dimensional change for long-term passage, as described in the following Non-Patent Document 1, i.e., the zero-expansion glass material has a problem with dimensional long-term stability.
Meanwhile, as for a cordierite-based sintered body consisting primarily of cordierite, which is a subject matter of the present invention, the following Patent Documents 1 and 2 disclose a dense cordierite-based low-expansion sintered body containing a rare-earth oxide in an amount of 0.3 to 8 mass % or 0.01 to 10 mass %. However, this sintered body is never usable as a mirror substrate because of its porosity of several %, and a thermal expansion coefficient thereof is not sufficiently reduced.
The following Patent Document 3 discloses a low-thermal expansion black ceramics containing 80 mass % or more of cordierite and usable as position measuring mirrors of stage. In this Document, it is mentioned that a maximum void diameter of the ceramics is preferably 5 μm or less. In fact, in Example of the Patent Document 3, it is described that a measured value of the maximum void diameter was several μm. However, the ceramics having such a large void is incapable of obtaining a significantly smooth polish-finished surface having a Ra of 1 nm or less. In the Patent Document 3, a rare-earth oxide, such as Y2O3 or Yb2O3, added in an amount of 1 to 10 mass %, is precipitated as a crystal phase of silicate (RE2O3.SiO2, wherein RE is a rare-earth element) or disilicate (RE2O3.2 SiO2). In such a sintered body having a mixture of a cordierite crystal phase and a crystal phase different therefrom, a micro-difference in polishing rate of precision polishing occurs between the crystals due to differences in hardness and chemical stability therebetween, which causes microscopic surface irregularities and therefore difficulty in achieving a smooth finished surface having a Ra of 1 nm or less.
The following Parent Document 4 discloses a dense low-thermal expansion ceramics containing 80 mass % or more of cordierite and usable as position measuring mirrors of stage. In the Parent Document 4, there is no description of whether a rare-earth oxide, such as Y2O3 or Yb2O3, added in an amount of 1 to 20 mass %, is formed as a silicate or disilicate crystal. However, a maximum void diameter is defined to be 5 μm or less, and, in Example, it is described that an observed value of the maximum void diameter was 0.7 μm at the minimum. Such a void occurs because it fails to adequately adjust a ratio between respective ones of SiO2, MgO and Al2O3 as primary components of cordierite. The existence of such a void makes it impossible to achieve a significantly smooth polish-finished surface having a Ra of 1 nm or less.
The following Patent Documents 5 to 7 disclose a mirror made of a low-thermal expansion ceramics and designed for position measurement or astronomical telescopes. The low-thermal expansion ceramics in the Patent Documents 5 to 7 is characterized in that it comprises a composite material prepared by combining: a first material which is one or more selected from the group consisting of lithium aluminosilicate, zirconium phosphate and cordierite; and a second material which is one or more selected from the group consisting of silicon carbide, silicon nitride, sialon, alumina, zirconia, mullite, zircon, aluminum nitride, calcium silicate and B4C, wherein an average surface roughness (Ra) of the ceramics is defined to be 10 nm or less.
In the Patent Documents 5 to 7, it is mentioned that a composite material of β-eucryptite and silicon carbide is preferable. However, in such a composite material prepared by mixing two or more materials largely different in hardness as in the Patent Documents 5 to 7, a micro-difference in polishing rate of precision polishing occurs between the materials, which causes microscopic surface irregularities and therefore difficulty in achieving a smooth finished surface having an average surface roughness (Ra) of 1 nm or less. In fact, in the Patent Documents 5 to 7, only a significantly rough polished surface having a Ra of 6 to 10 nm can be obtained.
Moreover, in a polycrystalline body having a mixture of two crystal grains largely different in thermal expansion coefficient, a residual stress caused by a difference in thermal expansion between the crystal grains formed during sintering of the materials remains in an obtained sintered body, which causes a problem that a secular change in shape of the sintered body is likely to occur, and, particularly, a large change in the shape occurs when the sintered body undergoes a temperature cycle of several ten ° C.